Harmonic generation of ultraintense laser pulses in underdense plasma

We propose a nonlinear theory of the generation of harmonic radiation from the interaction of ultraintense laser beams with plasma. The harmonic generation is related to the transition of the laser-plasma equilibrium state. By taking into account correlations among sidebands, we study many sidebands comprehensively. The harmonic generation is viewed as a redistribution of laser field over different frequencies because of the requirement of system stability. We introduce a system parameter S that is related to the sideband intensity spectrum and self-consistently calculate the value of S. Our numerical experiments reveal that the variations of controllable system parameters, plasma density, and laser peak intensity have a great effect on S.